Method and system of diversity transmission of data employing M-point QAM modulation

ABSTRACT

A method ( 600 ) of communicating a plurality of data bits over L diversity channels uses a constellation set comprising a plurality (L) of M-point quadrature amplitude modulation (QAM) constellations corresponding to the L diversity channels. The constellations do not exhibit overlapping data points, and provide full diversity. The method includes mapping ( 650 ) k*L data bits to L QAM transmission symbols in the L QAM constellation sets, and transmitting ( 660 ) the L QAM symbols where M=2 k * L . Each of each of the k*L data bits is directly mapped into all of the L QAM symbols of the QAM constellation set, and for all combinations of k*L bits, changing a value of one of k*L data bits changes all of the L symbols.

This invention pertains to the digital communication systems andmethods, and more particularly, to a method and system of diversitytransmission of data.

It is well known that wireless communications channels are subject tomultipath fading and Doppler effect.

Diversity transmission may be employed to mitigate the effects ofchannel fading. According to the basic diversity transmission method,multiple copies of transmission data are transmitted over multiplediversity channels. These diversity channels may be separated from eachother in time, frequency, space, or a combination of these domains. Atthe receiver, a more reliable estimate of the transmitted data isobtained by combining the information available in the copies receivedover the multiple parallel diversity channels.

The down side of the basic diversity technique is that the bandwidthefficiency is reduced. To achieve diversity gain without a loss intransmission rate, a form of signal space diversity or lattice codingcan be used. One drawback of these schemes, however, is their highcomputational complexity at the receiver.

A simpler full rate signal space diversity technique is the use of CodeDivision Multiplexing (CDM). In this method, L symbols are spread over Ldiversity channels using an orthogonal transform. Usually either aHadamard or Fourier transform is used. These transforms are preferredsince they can be implemented at the transmitter with little complexityusing a Fast Hadamard Transform (FHT) or a Fast Fourier Transform (FFT).

However, when these signals are transmitted over the diversity channels,the difference in the fading characteristics of the diversity channelsruins the orthogonality of the codes, creating self-interference (SI)and making accurate signal detection complex. To detect the transmittedsignal in the presence of SI, the optimal Maximum Likelihood (ML)detection method is to detect each bit using the Log-Likelihood Ratio(LLR). Unfortunately, the computation of the LLR for these complexsignals is not practical. Alternatively, it is also possible to despreadthe received data symbols and then use an interference cancellationscheme that iteratively estimates the amount of self-interference andremoves it from the received symbols. However, such interferencecancellation methods also involve considerable computational complexity.It is also possible to implement a simple receiver using Zero Forcing(ZF) or Minimum Mean Square Error (MMSE) equalization. However, thesemethods do not result in good performance.

Furthermore, the CDM scheme using simple Hadamard or Fourier transformscannot achieve a full degree of diversity. This is due to the fact thatthese spreading transforms result in overlapping constellation points.In other words, two different sets of data symbols spread using thesecodes can result in the same transmission symbol on one or morediversity channels. FIG. 1 illustrates a 256 point constellationproduced by Hadamard spreading of 4 QPSK symbols over 4 diversitychannels, where it can be seen that there is substantial overlap ofconstellation points.

A method has been proposed where QPSK modulated data symbols are rotatedbefore spreading. The use of this method avoids overlapping of thetransmit symbols, and thus, it can achieve full degree of diversity. Ifan optimum ML receiver is implemented, significantly better performanceis obtained.

FIG. 2 shows a 256 point constellation produced by rotated Hadamardspreading of 4 QPSK symbols over 4 diversity channels.

However, the unusual constellation shape shown in FIG. 2 complicatesdetection of these signals. Optimal ML detection of these signalsrequires a high degree of computational complexity in the receiver.

Accordingly, it would be desirable to provide an improved transmissionmethod and system that provides a full degree of transmission diversity.It would be further desirable to provide a method and system ofdiversity transmission that facilitates the use of a low-complexityreceiver architecture. It would be still further desirable to provide alow-complexity receiver for detecting a full-diversity transmission. Thepresent invention is directed to addressing one or more of the precedingconcerns.

In one aspect of the invention, a method of communicating a plurality ofdata bits over L diversity channels, comprises: providing aconstellation set comprising a plurality (L) of M-point quadratureamplitude modulation (QAM) constellations corresponding to the Ldiversity channels; mapping k*L data bits to L QAM transmission symbolsin the L QAM constellation sets; and transmitting the L QAM symbols,where M=2^(k)*^(L); and wherein for all combinations of k*L bits,changing a value of one of k*L data bits changes all of the L symbols.

In another aspect of the invention, a receiver is adapted to receive k*Lbits transmitted over diversity channels having a plurality (L) ofM-point quadrature amplitude modulation (QAM) constellations. Thereceiver comprises: a channel estimator adapted to output therefrom aplurality (L) of estimates h_(l) of the channel gain for each symbol; asoft demapper adapted to receive the plurality (L) of symbols r_(l) andthe plurality (L) of channel estimates h₁ and outputting therefrom aplurality (k*L) of approximate log-likelihood ratios Λ′_(i) for the k*Ltransmitted bits; a deinterleaver adapted to deinterleave the pluralityof approximate log-likelihood ratios; and a decoder adapted to decodethe plurality of approximate log-likelihood ratios into the k*L receivedbits, wherein the soft demapper calculates the approximatelog-likelihood ratios Λ′_(i) for each of the k*L transmitted bits, foriε (1, . . . , k*L), using either: (1) only the in-phase components ofall of the plurality (L) of symbols r₁; or (2) only the quadraturecomponents of all of the plurality (L) of symbols r₁.

In yet another aspect of the invention, a method of communicating aplurality of data bits, comprises: providing a constellation setcomprising a plurality (L) of M-point quadrature amplitude modulation(QAM) constellations; mapping k*L data bits to L QAM transmissionsymbols in the L QAM constellation sets; and transmitting the L QAMsymbols, where M=2^(k)*^(L); and wherein each of the k*L data bits isdirectly mapped into all of the L QAM symbols of the QAM constellationset.

FIG. 1 shows a constellation map for a 256 point constellation producedby Hadamard spreading of 4 QPSK symbols over 4 diversity channels;

FIG. 2 shows a constellation map for a 256 point constellation producedby rotated Hadamard spreading of 4 QPSK symbols over 4 diversitychannels;

FIG. 3 shows a block diagram of a system for transmitting data over aplurality of diversity channels;

FIG. 4 shows a constellation map for a 256 point constellation producedby system employing a Multi-Quadrature Amplitude Modulation (Multi-QAM)transmission scheme;

FIG. 5 shows a graphical representation of the constellation set ofTable 2;

FIG. 6 is a flowchart illustrating a method of communicating a pluralityof data bits;

FIG. 7 shows a block diagram of a receiver for receiving datatransmitted over a plurality of diversity channels;

FIG. 8 shows the bit error rate (BER) performance of a number ofdifferent schemes for transmitting uncoded data over two diversitychannels, with four bits per channel;

FIG. 9 shows the bit error rate (BER) performance of a number ofdifferent schemes for transmitting coded data over two diversitychannels, with four bits per channel;

FIG. 10 shows the bit error rate (BER) performance of a number ofdifferent schemes for transmitting uncoded data over four diversitychannels, with two bits per channel;

FIG. 11 shows the bit error rate (BER) performance of a number ofdifferent schemes for transmitting coded data over four diversitychannels, with two bits per channel.

The description to follow pertains to a new system and method ofquadrature amplitude modulation (QAM) referred to herein as “Multi-QAM,”and to systems and methods of transmitting and receiving data modulatedusing Multi-QAM. In the Multi-QAM scheme, data bits are directly mappedinto multiple M-ary QAM (M-QAM) transmission symbols. Beneficially, insuch a scheme L diversity channels correspond to L constellations havingno overlapping points, providing full transmission diversity.Beneficially, each of the L constellations is a square M-QAMconstellation.

In the discussion below, the following definitions apply:

C^((l)) is a QAM constellation for the l^(th) diversity channel;

M is the number of points in each QAM constellation (M-QAMconstellation);

m is a unique message to be transmitted;

s^((l)) _(m) is the symbol transmitted on the l^(th) diversity channelrepresenting message m;

S is the vector describing all the transmission symbols s^((l)) _(m);and

b(i,j) is the Hamming distance between two messages i and j.

Furthermore, in the discussion to follow, we assign the followingvariables:

L is the number of diversity channels, and therefore also the number oftransmission symbols (one transmission symbol per diversity channel),and the number of M-QAM constellations (one constellation per channel);and

k is the number of data bits to be transmitted per diversity channel.

In that case:M=2^(kL);  (1)S _(m) =[s ⁽⁰⁾ _(m) , . . . ,s ^((L−1)) _(m)]; and  (2)C ^((l)) ={s _(m) ⁽⁰⁾ |m=0, . . . ,M−1}.  (3)

FIG. 3 shows a block diagram of a transmission system 300 fortransmitting data over a plurality of diversity channels using Multi-QAMmodulation. The transmission system 300 includes an encoder 310, aninterleaver 320, a serial-parallel converter 330, and a Multi-QAMmodulator 340.

Optionally, in alternative embodiments, the transmission system may notcode and/or interleave the data, in which case encoder 310 and/orinterleaver 320 may be omitted.

Encoder 310 receives “raw” data and codes it with an error-correctioncode to facilitate accurate data recovery at the receiver side when thetransmission channel causes bit errors due to noise or interference(e.g., multipath interference). In other words, encoder 310 addsadditional “redundancy” bits to the data stream according to a setalgorithm, and the receiver has a priori knowledge of the codingalgorithm which allows it to recover the raw data with a reduced biterror rate. A variety of error correction codes may be employed.Beneficially, encoder 310 may implement a convolutional code or apunctured convolution code (e.g., ¾ rate punctured convolutional code).

Interleaver 320 interleaves the coded data in time. That is, interleaver320 redistributes the order of the encoded data bits according to a setpattern so that bits that are “adjacent” in the raw data stream areseparated in the interleaved bit stream. Meanwhile, the receiver has apriori knowledge of the interleaving algorithm which allows itdeinterleave the received data bits to their proper order in the datastream. By interleaving the data this way, the ability of the receiverto correct for data errors, particularly burst errors, is improved. Thebit error rate reducing effect of encoder 310 is enhanced by its use inconjunction with interleaver 320.

Serial-parallel converter 330 receives the interleaved, encoded, serialdata and outputs the bits in parallel, one parallel group of k*L databits at a time, where L is the number of diversity channels employed bythe system, and k is the number of bits to be transmitted per symbol foreach diversity channel.

Optionally, the coded, interleaved data may be provided in parallel totransmission system 300. For example, the data may have already beencoded and optionally interleaved, and then stored on a data storagemedium. Then when it is time to transmit the data, the encoded andinterleaved data may be read out from the storage medium and provided tothe Multi-QAM transmission system. The data may be read out in parallelgroups of k*L bits. In that case, one or more components among the coder310, interleaver 320, and serial-parallel converter 330 may be omittedfrom the transmission system 300, their functions having been alreadyequivalently performed by one or more external components.

Multi-QAM modulator 340 receives the k*L parallel data bits andgenerates a total of L M-QAM transmission symbols, S_(m)=[s⁽⁰⁾ _(m), . .. , s^((L−1)) _(m)], to be transmitted on the L diversity channels, withone M-QAM transmission symbol being transmitted on each diversitychannel.

In particular, Multi-QAM modulator 340 directly maps the k*L data bitsinto all of the L M-QAM transmission symbols, each M-QAM transmissionsymbol belonging to one of L square M-QAM constellations correspondingto the L diversity channels, where M=2^(kL). For example, when k is two(2) and L is four (4), then (k, L) is (2, 4) and M is 256. That is, inthat case each of the L diversity channels has its own 256 point squareM-QAM constellation. Beneficially, the constellations do not exhibitoverlapping data points. In one embodiment, Multi-QAM modulator 340implements the M-QAM symbol generation using one or more look-up tables(e.g., one look-up table for each of the L channels).

Significantly, the Multi-QAM constellation set is designed such thatchanging any one of the k*L data bits will in turn change the M-QAMtransmission symbols in all of the L M-QAM constellations.

FIG. 4 shows a constellation map for a 256 point M-QAM constellationproduced by Multi-QAM modulator 340. As can be seen, advantageously noneof the 256 points in the constellation of FIG. 4 overlap each other.

Beneficially, the constellation set for Multi-QAM modulator 340 isselected to be symmetrical. That is, if, for a given message m thetransmission symbols are defined by a vector S_(m), then for a messagem=(2^(kL)−1−m) the symbols are defined by the vector −S_(m).

Beneficially, the constellations exhibit good distance properties andestablish an upper bound on the bit error rate (BER) performance of thesystem. To achieve these parameters within the symmetric constellationsets, beneficially a constellation set for Multi-QAM modulator 340 ischosen to minimize Ω_(C), where:

$\begin{matrix}{\Omega_{C} = {\sum\limits_{i \neq j}\;{\frac{b\left( {i,j} \right)}{\prod\limits_{l = 0}^{L - 1}\;{{S_{i}^{(l)} - S_{j}^{(l)}}}^{2}}.}}} & (4)\end{matrix}$

Also beneficially, the in-phase (I) and quadrature (Q) components ofeach constellation in the constellation set use the same constellationpoints. This simplifies the receiver design, as discussed in furtherdetail below.

Through an exhaustive search, the following specific cases have beenidentified.

When k=3, L=2, beneficially the in-phase (I) and quadrature (Q)components of the constellation set are each defined by Table 1, below.

TABLE 1 M 0 1 2 3 4 5 6 7 s⁽⁰⁾ _(m) −7 −5 −1 −3 3 1 5 7 s⁽¹⁾ _(m) 3 −5 7−1 1 −7 5 −3

When k=2, L=3, beneficially the in-phase (I) and quadrature (Q)components of the constellation set are each defined by Table 2, below.

TABLE 2 M 0 1 2 3 4 5 6 7 s⁽⁰⁾ _(m) −7 −3 −1 −5 5 1 3 7 s⁽¹⁾ _(m) 3 −1 7−5 5 −7 1 −3 s⁽²⁾ _(m) 1 7 −3 −5 5 3 −7 −1

When k=4, L=2, beneficially the in-phase (I) and quadrature (Q)components of the constellation set are each defined by Table 3, below.

TABLE 3 m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 s⁽⁰⁾ _(m) −15 −13 −11 −9−3 −1 −7 −5 5 7 1 3 9 11 13 15 s⁽¹⁾ _(m) −1 11 −7 5 −3 9 −13 15 −15 13−9 3 −5 7 −11 1

When k=2, L=4, the process of finding a suitable constellation setbecomes computationally difficult.

FIG. 5 shows a graphical representation of the constellation set ofTable 2. Inspection of FIG. 5 reveals a significant feature of theconstellation set. For example, one sees that the symbol s₀ ⁽⁰⁾ for theconstellation C⁽⁰⁾ has a value of −7, and the symbol s₀ ⁽¹⁾ for theconstellation C⁽¹⁾ has a value of 3. Meanwhile, the symbol s₅ ⁽¹⁾ forthe constellation C⁽¹⁾ also has a value of −7, and the symbol s₅ ⁽²⁾ forthe constellation C⁽²⁾ also has a value of 3. Similarly, the symbol s₁⁽⁰⁾ for the constellation C⁽⁰⁾ has a value of −3, and the symbol s₁ ⁽¹⁾for the constellation C⁽¹⁾ has a value of −1. Meanwhile, the symbol S₇⁽¹⁾ for the constellation C⁽¹⁾ also has a value of −3, and the symbol S₇⁽²⁾ for the constellation C⁽²⁾ also has a value of −1.

In general, inspection of FIG. 5 reveals that the permutation to reachfrom any constellation, C^((l)) to the next constellation C^((l+1)) isthe same for all l.

So, for the case where k=2, L=4, by concentrating on symmetricalconstellation sets where the permutation to reach from anyconstellation, C^((l)) to the next constellation C^((l+1)) is the samefor all l, and searching for a constellation set that minimizes Ω_(C),one finds the constellation set where the in-phase (I) and quadrature(Q) components of the constellation set are each defined by Table 4,below.

TABLE 4 m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 s⁽⁰⁾ _(m) −15 −9 −1 −13−5 −11 3 −7 7 −3 11 5 13 1 9 15 s⁽¹⁾ _(m) −5 −15 13 7 3 −1 9 11 −11 −9 1−3 −7 −13 15 5 s⁽²⁾ _(m) 3 −5 −7 −11 9 13 15 1 −1 −15 −13 −9 11 7 5 −3s⁽³⁾ _(m) 9 3 11 −1 15 −7 5 −13 13 −5 7 −15 1 −11 −3 −9

FIG. 6 shows a flowchart of a method of communicating data using asystem such as the system 300 shown in FIG. 3.

In a first step 610, “raw” data is coded with an error-correction codeto facilitate accurate data recovery at the receiver side when thetransmission channel causes bit errors due to noise or channel effects(e.g., multipath fading). A variety of error correction codes may beemployed. Beneficially, the encoder may implement a convolutional codeor a punctured convolution code (e.g., ¾ rate punctured convolutionalcode).

In a step 620, the coded data is interleaved.

In a step 630, the coded, interleaved data is converted from a serialdata stream to a parallel set of k*L parallel data bits.

Optionally, the coded, interleaved data may be provided in parallel tothe transmission system. For example, the data may have already beencoded, interleaved, and stored on a data storage medium, and then whenready for transmission, it may be read out in parallel from the storagemedium and provided to the Multi-QAM transmission system.

In a step 640, a Multi-QAM modulator is provided with a constellationset comprising a plurality (L) of M-point quadrature amplitudemodulation (M-QAM) constellations. Beneficially, the constellations donot exhibit overlapping data points. The M-QAM constellation set may beprovided in the form or one or more look-up tables.

Significantly, the M-QAM constellation set provides that for allcombinations of k*L data bits received by the Multi-QAM modulator,changing any one of the k*L data bits will in turn change the M-QAMtransmission symbols in all of the L M-QAM constellations.

Beneficially, the M-QAM constellations in the M-QAM constellation setexhibit good distance properties and establish an upper bound on the biterror rate (BER) performance of the system. Also beneficially, the M-QAMconstellation set is selected to be symmetrical. Furthermore,beneficially the in-phase (I) and quadrature (Q) components of eachM-QAM constellation in the M-QAM constellation set use the sameconstellation points. To achieve these parameters, beneficially an M-QAMconstellation set for the Multi-QAM modulator is chosen to minimizeΩ_(C) (equation 4). The in-phase (I) and quadrature (Q) components ofthe M-QAM constellation set may each correspond to any one of theconstellation sets shown in Tables 1-4 above.

In a step 650, the Multi-QAM modulator maps the k*L data bits to L M-QAMtransmission symbols in the L M-QAM constellation sets. Each of the k*Ldata bits is directly mapped into all of the L M-QAM symbols of theM-QAM constellation set.

Then, in a step 660, the L M-QAM symbols are transmitted.

At the receiver, regardless of whether hard or soft decisions are used,for optimal maximum likelihood (ML) detection of the original data bits,the Log-Likelihood Ratio (LLR) or each bit must be calculated. Assumethat diversity channel l is modeled by:r _(l) =h _(l) *x _(l) +n _(l),  (5)

where r_(l) is the received symbol from diversity channel l, h_(l) isthe complex channel gain for diversity channel l, x_(l) is theoriginally transmitted symbol for diversity channel l belonging toconstellation C^((l)), and n_(l) is the complex additive white Gaussiannoise (AWGN) having variance σ². In that case, the LLR, Λ_(i), for thei^(th) transmitted bit is:

$\begin{matrix}{\Lambda_{i} = \frac{\sum\limits_{m \in A_{1}}{\exp\left( {{- \frac{1}{2\;\sigma^{2}}}{\sum\limits_{l = 0}^{L - 1}{{r_{l} - {h_{l}*s_{m}^{(l)}}}}^{2}}} \right)}}{\sum\limits_{m \in A_{0}}{\exp\left( {{- \frac{1}{2\;\sigma^{2}}}{\sum\limits_{l = 0}^{L - 1}{{r_{l} - {h_{l}*s_{m}^{(l)}}}}^{2}}} \right)}}} & (6)\end{matrix}$where iε(1, . . . , k*L), A_(o) contains all messages where bit i=0, andA₁ contains all messages where bit i=1.

Unfortunately, exact calculation of equation (6) for each received bitis very complex and not suitable for a practical receiverimplementation.

However, advantageously, because of properties of the M-QAMconstellations used in the Multi-QAM transmission (e.g., symmetry;separation of bits on in-phase and quadrature channels; etc.), asignificantly simpler demapper may be employed which provides anexcellent approximation of the LLR Λ_(i).

Beneficially, a receiver calculates the approximate the approximate LLR,Λ′_(i), of each bit according to following formulas:

$\begin{matrix}{{\Lambda_{iR}^{\prime} = {{\sum\limits_{l = 0}^{L - 1}\left( {z_{R,l} - {{h_{l}}s_{R,{m0}_{R}}^{l}}} \right)^{2}} - {\sum\limits_{l = 0}^{L - 1}\left( {z_{R,l} - {{h_{l}}s_{R,{m\; 1_{R}}}^{l}}} \right)^{2}}}}{and}} & (7) \\{{\Lambda_{iI}^{\prime} = {{\sum\limits_{l = 0}^{L - 1}\left( {z_{I,l} - {{h_{l}}s_{I,{m\; 0_{I}}}^{l}}} \right)^{2}} - {\sum\limits_{l = 0}^{L - 1}\left( {z_{I,l} - {{h_{l}}s_{I,{m\; 1_{I}}}^{l}}} \right)^{2}}}},} & (8)\end{matrix}$

where Λ′_(iR) is the approximate log-likelihood ratio for a bitmodulated using in-phase components of the QAM symbols;

where Λ′_(iI) is the approximate log-likelihood ratio for a bitmodulated using quadrature components of the QAM symbols;

where z is

$\frac{r_{l}h_{l}^{*}}{h_{l}},$

where m_(0R) is the message among all messages m where the bit i=0 thatminimizes

${\sum\limits_{l = 0}^{L - 1}\left( {z_{R,l} - {{h_{l}}s_{R,m}^{l}}} \right)^{2}},$

where m_(1R) is the message the message among all messages m where thebit i=1 that minimizes

${\sum\limits_{l = 0}^{L - 1}\left( {z_{R,l} - {{h_{l}}s_{R,m}^{l}}} \right)^{2}},$

where m_(0I) is the message m among all messages where the bit i=0 thatminimizes

${\sum\limits_{l = 0}^{L - 1}\left( {z_{I,l} - {{h_{l}}s_{I,m}^{l}}} \right)^{2}},$

where m_(1I) is the message the message m among all messages where thebit i=1 that minimizes

${\sum\limits_{l = 0}^{L - 1}\left( {z_{I,l} - {{h_{l}}s_{I,m}^{l}}} \right)^{2}},$

where S^(l) _(R,m) is the in-phase component of a symbol transmittedover the l^(th) diversity channel for message m, and

where S^(l) _(I,m) is the quadrature component of a symbol transmittedover the l^(th) diversity channel for message m.

FIG. 7 shows a block diagram of a receiver 700 for receiving datatransmitted over a plurality of diversity channels using Multi-QAM.Receiver 700 comprises channel estimator 710, soft demapper 720,parallel-to-serial converter 730, deiniterleaver 740, and decoder 750.

Optionally, in alternative embodiments, the transmitted data may not becoded and/or interleaved, in which case deiniterleaver 740 and/ordecoder 750 may be omitted.

Channel estimator 710 outputs a plurality (L) of estimates h_(l) of thecomplex channel gain for the diversity channel l through a correspondingM-QAM symbol r_(l) was received. Any of a variety of known channelestimator algorithms may be employed. For example, the channel estimator710 may estimate the channel from a received set of training symbolswhich are known a priori to receiver 700. Optionally, it is possiblethat channel estimator 710 receives a plurality (L) of M-QAM symbolsr_(l) and estimates the channel characteristics therefrom.

Soft demapper 720 receives the plurality (L) of symbols r_(l) and theplurality (L) of channel estimates h_(l) and outputs therefrom aplurality (k*L) of approximate log-likelihood ratios Λ′_(i) for the k*Ltransmitted bits that produced the L received M-QAM symbols r_(l). Softdemapper 720 calculates the approximate log-likelihood ratios for eachof the k*L transmitted bits, for iε(1, . . . , k*L), using either: (1)only the in-phase components of all of the plurality (L) of symbolsr_(l); or (2) only the quadrature components of all of the plurality (L)of symbols r_(l). Beneficially, the soft demapper 720 calculates theapproximate log-likelihood ratios Λ′_(i) according to equations (7) and(8) above.

Parallel-to-serial converter 730 receives the plurality (k*L) ofapproximate log-likelihood ratios Λ′_(i) for the k*L transmitted bits inparallel, and converts them to a serial data stream of approximatelog-likelihood ratios, Λ′_(i). Optionally, soft demapper 720 may bedesigned in such a way that it automatically outputs the approximatelog-likelihood ratios Λ′_(i) as a plurality (k*L) of parallel outputs,in which case parallel-to-serial converter 730 may be omitted.

Deiniterleaver 740 receives the serial data stream of approximatelog-likelihood ratios Λ′_(i) and deinterleaves the approximatelog-likelihood ratios Λ′_(i) to correspond to the original order of thedata before it was interleaved on the transmit side.

Decoder 750 receives the deinterleaved log-likelihood ratios Λ′_(i) andapplies an error correction decoding algorithm to detect the received“raw” data bits. Beneficially, decoder 750 may decode the data using aViterbi type decoder. Beneficially, decoder 750 uses “soft” decisiondecoding of the approximate log-likelihood ratios Λ′_(i).

FIG. 8 shows the bit error rate (BER) performance of a number ofdifferent schemes for transmitting uncoded data over two diversitychannels, with four bits per channel. In particular, FIG. 8 depicts theuncoded performance of the Multi-QAM scheme with (k,L)=(4, 2) andcompares it to the BER performance of 16-QAM without diversity, 16-QAMmodulation with diversity L=2 (½ rate), and rotated Hadamard spreading,where 16-PSK symbols have been used before spreading to allow thetransmission of k=4 bits per diversity channel. The performance of theMulti-QAM modulation is given both using an optimal demapper of equation(6), and the approximation provided in equations (7) and (8). We observethat the approximations used to simplify the demapper 720 do not resultin noticeable loss in performance. By comparing the slope of the BERcurves for Multi-QAM and rotated Hadamard spreading, to that of the16-QAM with simple diversity, we can see that both schemes achieve fulldiversity. Furthermore, we observe that Multi-QAM performs better thanthe rotated Hadamard.

FIG. 9 shows the bit error rate (BER) performance of the same modulationschemes shown in FIG. 8 for transmitting coded data over two diversitychannels, with four bits per channel, where an industry standard ¾ ratepunctured convolutional code is used. A block interleaver of sufficientlength to decorrelate channel errors has been employed. At the receivera Viterbi algorithm uses soft decisions to decode the data bits. We cansee that at a BER of 10⁻⁶, Multi-QAM shows a gain of approximately 1.5dB compared to the 16-QAM.

FIGS. 10 and 11 show the simulated uncoded and coded BER results forMulti-QAM modulation with (k,L)=(2, 4). These results are compared withthose of QPSK modulation without diversity, QPSK modulation withdiversity L=4 (¼ rate), and rotated Hadamard spreading. Once again weobserve that full degree of diversity is achieved. We also observe thata BER of 10−6, the proposed Multi-QAM performs 4.2 dB better compared tothe QPSK modulation. However, it performs 0.5 dB worse than the rotatedHadamard. On the other hand, considering that the proposed scheme can beimplemented at significantly lowered complexity, it still showsdesirable performance.

While preferred embodiments are disclosed herein, many variations arepossible which remain within the concept and scope of the invention.Such variations would become clear to one of ordinary skill in the artafter inspection of the specification, drawings and claims herein. Theinvention therefore is not to be restricted except within the spirit andscope of the appended claims.

1. A method of communicating a plurality of data bits over L diversity channels, comprising: providing a constellation set comprising a plurality (L) of M-point quadrature amplitude modulation (QAM) constellations corresponding to the L diversity channels; mapping k*L data bits to L QAM transmission symbols in the L QAM constellation sets; and transmitting the L QAM symbols over said respective L diversity channels, where M=2^(k)*^(L); and wherein for all combinations of k*L bits, changing a value of one of k*L data bits changes all of the L symbols.
 2. The method of claim 1, wherein the constellation set minimizes Ω_(C), where $\Omega_{C} = {\sum\limits_{i \neq j}{\frac{b\left( {i,j} \right)}{\prod\limits_{l = 0}^{L - 1}{{S_{i}^{(l)} - S_{j}^{(l)}}}^{2}}.}}$
 3. The method of claim 1, wherein, when for any message m the symbols are defined by a vector S_(m), then for a message m=(2^(kL)−1−m), the symbols are defined by the vector −S_(m).
 4. The method of claim 1, where k=3, L=2, and where the in-phase (I) and quadrature (Q) components of the constellation set are each defined by the following table: m 0 1 2 3 4 5 6 7 s⁽⁰⁾ _(m) −7 −5 −1 −3 3 1 5 7 s⁽¹⁾ _(m) 3 −5 7 −1 1 −7 5 −3.


5. The method of claim 1, where k=2, L=3, and where the in-phase (I) and quadrature (Q) components of the constellation set are each defined by the following table: m 0 1 2 3 4 5 6 7 s⁽⁰⁾ _(m) −7 −3 −1 −5 5 1 3 7 s⁽¹⁾ _(m) 3 −1 7 −5 5 −7 1 −3 s⁽²⁾ _(m) 1 7 −3 −5 5 3 −7 −1.


6. The method of claim 1, where k=4, L=2, and where the in-phase (I) and quadrature (Q) components of the constellation set are each defined by the following table: m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 s⁽⁰⁾ _(m) −15 −13 −11 −9 −3 −1 −7 −5 5 7 1 3 9 11 13 15 s⁽¹⁾ _(m) −1 11 −7 5 −3 9 −13 15 −15 13 −9 3 −5 7 −11
 1.


7. The method of claim 1, where k=2, L=4, and where the in-phase (I) and quadrature (Q) components of the constellation set are each defined by the following table: m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 s⁽⁰⁾ _(m) −15 −9 −1 −13 −5 −11 3 −7 7 −3 11 5 13 1 9 15 s⁽¹⁾ _(m) −5 −15 13 7 3 −1 9 11 −11 −9 1 −3 −7 −13 15 5 s⁽²⁾ _(m) 3 −5 −7 −11 9 13 15 1 −1 −15 −13 −9 11 7 5 −3 s⁽³⁾ _(m) 9 3 11 −1 15 −7 5 −13 13 −5 7 −15 1 −11 −3 −9.


8. A receiver for receiving k*L bits transmitted over diversity channels comprising a plurality (L) of M-point quadrature amplitude modulation (QAM) constellations, the receiver comprising: a channel estimator adapted to output a plurality (L) of estimates h_(l) of the channel gain for each symbol; a soft demapper adapted to receive the plurality (L) of symbols r_(l) and the plurality (L) of channel estimates h_(l) and to output therefrom a plurality (k*L) of approximate log-likelihood ratios Λ_(i)′ for the k*L transmitted bits; a deinterleaver adapted to deinterleave the plurality of approximate log-likelihood ratios; and a decoder adapted to decode the plurality of log-likelihood ratios into the k*L received bits, wherein the soft demapper calculates the approximate log-likelihood ratios Λ_(i)′ for each of the k*L transmitted bits, for iε(1, . . . , k*L), using either: (1) only the in-phase components of all of the plurality (L) of symbols r_(l); or (2) only the quadrature components of all of the plurality (L) of symbols r_(l).
 9. The receiver of claim 8, wherein the soft demapper demaps the symbols r_(l) into the log-likelihood ratios κ_(i)′ according to the formulas: $\begin{matrix} {{\Lambda_{iR}^{\prime} = {{\sum\limits_{l = 0}^{L - 1}\left( {z_{R,l} - {{h_{l}}s_{R,{m0}_{R}}^{l}}} \right)^{2}} - {\sum\limits_{l = 0}^{L - 1}\left( {z_{R,l} - {{h_{l}}s_{R,{m\; 1_{R}}}^{l}}} \right)^{2}}}}{and}} \\ {{\Lambda_{iI}^{\prime} = {{\sum\limits_{l = 0}^{L - 1}\left( {z_{I,l} - {{h_{l}}s_{I,{m\; 0_{I}}}^{l}}} \right)^{2}} - {\sum\limits_{l = 0}^{L - 1}\left( {z_{I,l} - {{h_{l}}s_{I,{m\; 1_{I}}}^{l}}} \right)^{2}}}},} \end{matrix}$ where Λ_(iR)′ is an approximate log-likelihood ratio for a bit modulated using in-phase components of the QAM symbols; where Λ_(iI)′, is an approximate log-likelihood ratio for a bit modulated using quadrature components of the QAM symbols; where z is $\frac{r_{l}h_{l}^{*}}{h_{l}},$ where m_(0R) is the message among all messages m where the bit i=0 that minimizes ${\sum\limits_{l = 0}^{L - 1}\left( {z_{R,l} - {{h_{l}}s_{R,m}^{l}}} \right)^{2}},$ where m_(1R) is the message the message among all messages m where the bit i=1 that minimizes ${\sum\limits_{l = 0}^{L - 1}\left( {z_{R,l} - {{h_{l}}s_{R,m}^{l}}} \right)^{2}},$ where m_(0I) is the message m among all messages where the bit i=0 that minimizes ${\sum\limits_{l = 0}^{L - 1}\left( {z_{I,l} - {{h_{l}}s_{I,m}^{l}}} \right)^{2}},$ where m_(1I) is the message the message m among all messages where the bit i=1 that minimizes ${\sum\limits_{l = 0}^{L - 1}\left( {z_{I,l} - {{h_{l}}s_{I,m}^{l}}} \right)^{2}},$ where S^(l) _(R,m) is the in-phase component of a symbol transmitted over the l^(th) diversity channel for message m, and where S^(l) _(I,m) is the quadrature component of a symbol transmitted over the l^(th) diversity channel for message m.
 10. The receiver of claim 8, further comprising a parallel-to-serial converter adapted to receive in parallel the plurality (k*L) of approximate log-likelihood ratios Λ_(i)′ from the soft demapper and to output a serial data stream comprising the plurality (k*L) of approximate log-likelihood ratios Λ_(i)′.
 11. The receiver of claim 8, where the decoder performs a Viterbi error correction algorithm using soft decisions.
 12. A method of communicating a plurality of data bits over L diversity channels, comprising: providing a constellation set comprising a plurality (L) of M-point quadrature amplitude modulation (QAM) constellations corresponding to the L diversity channels; mapping k*L data bits to L QAM transmission symbols in the L QAM constellation sets; and transmitting the L QAM symbols over said respective L diversity channels, where M=2^(k)*^(L); and wherein each of the k*L data bits is directly mapped into all of the L QAM symbols of the QAM constellation set.
 13. The method of claim 12, further comprising: encoding “raw” data with an error-correction code; interleaving the encoded data; and converting the coded, interleaved data from a serial data stream to a parallel set of k*L parallel data bits.
 14. The method of claim 12, wherein the constellation set minimizes Ω_(C), where $\Omega_{C} = {\sum\limits_{i \neq j}{\frac{b\left( {i,j} \right)}{\prod\limits_{l = 0}^{L - 1}{{S_{i}^{(l)} - S_{j}^{(l)}}}^{2}}.}}$
 15. The method of claim 12, wherein, when for any message m the symbols are defined by a vector S_(m), then for a message m=(2^(kL)−1−m), the symbols are defined by the vector −S_(m).
 16. The method of claim 12, where k=3, L=2, and where the in-phase (I) and quadrature (Q) components of the constellation set are each defined by the following table: m 0 1 2 3 4 5 6 7 s⁽⁰⁾ _(m) −7 −5 −1 −3 3 1 5 7 s⁽¹⁾ _(m) 3 −5 7 −1 1 −7 5 −3.


17. The method of claim 12, where k=2, L=3, and where the in-phase (I) and quadrature (Q) components of the constellation set are each defined by the following table: m 0 1 2 3 4 5 6 7 s⁽⁰⁾ _(m) −7 −3 −1 −5 5 1 3 7 s⁽¹⁾ _(m) 3 −1 7 −5 5 −7 1 −3 s⁽²⁾ _(m) 1 7 −3 −5 5 3 −7 −1.


18. The method of claim 12, where k=4, L=2, and where the in-phase (I) and quadrature (Q) components of the constellation set are each defined by the following table: m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 s⁽⁰⁾ _(m) −15 −13 −11 −9 −3 −1 −7 −5 5 7 1 3 9 11 13 15 s⁽¹⁾ _(m) −1 11 −7 5 −3 9 −13 15 −15 13 −9 3 −5 7 −11
 1.


19. The method of claim 12, where k=2, L=4, and where the in-phase (I) and quadrature (Q) components of the constellation set are each defined by the following table: m 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 s⁽⁰⁾ _(m) −15 −9 −1 −13 −5 −11 3 −7 7 −3 11 5 13 1 9 15 s⁽¹⁾ _(m) −5 −15 13 7 3 −1 9 11 −11 −9 1 −3 −7 −13 15 5 s⁽²⁾ _(m) 3 −5 −7 −11 9 13 15 1 −1 −15 −13 −9 11 7 5 −3 s⁽³⁾ _(m) 9 3 11 −1 15 −7 5 −13 13 −5 7 −15 1 −11 −3 −9. 